System and method for tape layout optimization

ABSTRACT

A tape layout module for determining a tape layout allocation strategy for laying out data on tape, the data being organized into a plurality of fixed-size subdata sets with each of the plurality of subdata sets including a plurality of codeword interleaves, the tape including a plurality of media defect characteristics, includes a tape layout optimization system including a processor that receives information on the plurality of media defect characteristics. The tape layout optimization system determines the tape layout allocation strategy based at least in part on at least one of the plurality of media defect characteristics. Additionally, the tape layout optimization system can determine the tape layout allocation strategy further based on distance spectra between pairs of the plurality of codeword interleaves. Further, the tape layout optimization system can determine the tape layout allocation strategy by selectively utilizing at least one tape layout parameter.

RELATED APPLICATION

The present application is a continuation application and claims thebenefit under 35 U.S.C. 120 on co-pending U.S. patent application Ser.No. 15/655,289, filed on Jul. 20, 2017. To the extent permitted, thecontents of U.S. patent application Ser. No. 15/655,289 is incorporatedherein by reference.

BACKGROUND

The Linear Tape Open (LTO) format is an open format magnetic tape datastorage technology that enables users to have access to multiple sourcesof storage media products that will be compatible with one another. Incurrent LTO tape drives, variable-length blocks of user data arereceived from a host interface and are segmented to create fixed-sizedata blocks or data sets. These data sets are further broken down intosmaller but equal-size units known as subdata sets (SDSs). An SDS istypically organized into a two-dimensional array of rows and columns ofdata symbols. Each row of data symbols in the two-dimensional array maybe made up of multiple interleaved data and parity symbols. ErrorCorrection Coding (ECC) is typically generated for each row and eachcolumn in the array to protect the data contained therein. Morespecifically, ECC parity bytes are generated for each row that areappended to each row to create multiple codewords (e.g., four for LTO 6and LTO 7 drives and likely to increase in future generations) thatinclude both data and parity symbols. Each row of encoded SDS isreferred to as one codeword interleave (CWI). Additionally, CWIs arealso encoded with ECC parity bytes for each column that are appended toeach column to generate vertical protection for the segmented user data,summing up to N CWIs per SDS.

The rows of each SDS, i.e., the CWIs, with the possibility of header andother metadata information having been added thereto, are distributedacross and along the tape in a number of passes called wraps. In eachwrap, based on the number of tracks T, CWIs are allocated to each tracksuch that spatially correlated errors or defects on the magnetic tapesurface will spread across multiple SDSs. Stated in another manner, inorder to ensure that the number of errors in an SDS do not overpower theECC codes used to protect the SDS, the rows of the SDS may be laid outon the magnetic tape in such a manner that, if errors occur spatiallyclose to one another on the tape medium, the errors will be spreadacross multiple SDSs in the data set. Thus, in an attempt to minimizethe burden on the ECC decoding of each SDS, such an allocation willideally even out the correlated errors that happen on magnetic tape bydistributing CWIs over the distinct SDSs. Limiting the number of errorsoccurring in an SDS increases the probability that the ECC parityassociated with the SDS will be powerful enough to correct the errorscontained therein.

Recent developments in multi-track LTO tape drive systems paved the wayfor storing petabytes of data at very low costs as part of the greenstorage context in large scale deployments. This performance gain is dueto various innovations that took place in further research for mediacharacteristics, tape mechanics, head technology, tribology and advancedsignal processing algorithms. Most of the today's tape technology relieson continuous operation in different conditions and environments inwhich the media and the data are subject to defective reads/writes andexternal wear and damage. Most of the survey data and experimentalobservations demonstrate that the majority of performance bottleneck isdue to such external repeatable defects and associated correlatedfailures such as dead tracks. Physical constraints of tape and theguarantee of operation under different environmental conditions have ledto advanced configurations such that the performances of signalprocessing and error correction coding algorithms are affected theleast. One of the genuine features of the LTO format is in the way codeddata is laid out along and across the magnetic tape surface.

In one application of such a tape layout process, LTO tape drives employa set of “randomization” methods (also sometimes referred to herein as“layout parameters”) in order to balance the distribution of CWIs on thetape surface. Such methods include, but are not limited to, trackrotations (transverse to the tape), CWI set swaps, track swaps andodd/even indexed SDS separations, which are designed to evenlydistribute CWIs on the tape and thereby decorrelate error locations onthe tape from error locations within each SDS. CWIs from an SDS may beperiodically swapped between even and odd data tracks because even datatracks and odd data tracks may have systematic differences. Suchsystematic differences may be the result of recording head design,electronics configuration, signal line routing, or the like.

One drawback that has been seen with such methods is that they do notsubstantially improve the separation distance between CWIs to achieveoptimal decorrelation. Subsequent efforts have proposed to maximize theminimum separation distance between CWIs belonging to the same SDS,while evening out the CWI set and track distribution, in order to makeeach SDS have almost the same decoding performance and datareconstruction reliability. Unfortunately, such subsequent efforts havealso experienced certain drawbacks, as optimal decorrelation of errorsis not always achieved depending upon the types of defects being seen.

SUMMARY

The present invention addresses a problem related to the present stateof LTO tape layout allocation strategies and methodologies (codewordallocation on the physical medium—concerning both logical and physicallayout design) and proposes an optimization procedure given the type,size and frequency of media defects and statistics. Accordingly, thepresent invention has been developed to provide an improved tape layoutdesign for reliable ECC decoding. More specifically, the presentinvention presents a generalized codeword layout and allocation strategyby exploring the distance spectra of encoded data set elements. Based onsuch layout constructions, the present invention endeavors to minimizeor otherwise limit the effect of media defects on the decodingperformance of the tape and correspondingly increase data retentionreliability. In particular, the present invention substantially improvessuch tape layout designs by incorporating side information such as mediadefect statistics into the optimization problem in order to achieve thebest ECC decoding performance for the given defect/error model ofinterest. Additionally, as provided herein, decoding performance of thetape consists of one independent decoding for each SDS. Thus, theobjective of the present invention is not only to limit the effect ofmedia defects, but also distribute the effect evenly between each of theindependent decodings.

In various embodiments, the present invention is directed toward a tapelayout module for determining a tape layout allocation strategy forlaying out data both logically and physically on tape, the data beingorganized into a plurality of fixed-size subdata sets with each of theplurality of subdata sets including a plurality of codeword interleaves,the tape including a plurality of media defect characteristics. In suchembodiments, the tape layout module includes a tape layout optimizationsystem including a processor that receives information on the pluralityof media defect characteristics. The tape layout optimization systemdetermines the tape layout allocation strategy based at least in part onat least one of the plurality of media defect characteristics. In someapplications, the plurality of media defect characteristics arereproducible.

In some embodiments, the tape layout optimization system determines thetape layout allocation strategy based at least in part on each of theplurality of media defect characteristics. Additionally, the tape layoutoptimization system can determine the tape layout allocation strategyfurther based on distance spectra between pairs of the plurality ofcodeword interleaves.

In certain embodiments, the tape layout optimization system generates aplurality of coefficients, α_(i)(b_(i)), that are the result of amodeling of the plurality of media defect characteristics. This may bedetermined and fixed for a given media type and manufacturing process.In some such embodiments, the tape layout optimization system determinesthe tape layout allocation strategy by computing a weighted separationcoefficient (WSC), WSC(s)=α₁(b₁) c₁+α₂(b₂) c₂+ . . . α_(U)(b_(U)) c_(U),where b_(i) represents the i-th unique element of a distance spectrabetween pairs of the plurality of codeword interleaves, c_(i) representsthe count of the unique element b_(i), and U represents the set of allpossible distances for a given layout.

Additionally, in some embodiments, the tape layout optimization systemdetermines the tape layout allocation strategy by selectively utilizingat least one tape layout parameter. Further, the tape layoutoptimization system can determine the tape layout allocation strategy byselectively utilizing a plurality of tape layout parameters. In certainsuch embodiments, the plurality of tape layout parameters are selectedfrom a group consisting of track swaps, codeword interleave set swaps,track rotations, and odd/even indexed subdata set separations.

The present invention is further directed toward a data flow system fora tape drive including (i) a data intake system that receives aplurality of variable-length data blocks from a host device; (ii) a datapreprocessing system that converts the plurality of variable-length datablocks into a plurality of fixed-size data sets, the data preprocessingsystem then converting the plurality of fixed-size data sets into aplurality of fixed-size subdata sets with each of the plurality ofsubdata sets including a plurality of codeword interleaves; and (iii)the tape layout module as described above that determines a tape layoutallocation strategy for laying out the plurality of codeword interleaveson tape.

Additionally, the present invention is further directed toward a methodfor determining a tape layout allocation strategy for laying out data ontape, the data being organized into a plurality of fixed-size subdatasets with each of the plurality of subdata sets including a plurality ofcodeword interleaves, the tape including a plurality of media defectcharacteristics, the method including the steps of (A) receivinginformation on the plurality of media defect characteristics with a tapelayout optimization system including a processor; and (B) determiningthe tape layout allocation strategy with the tape layout optimizationsystem based at least in part on at least one of the plurality of mediadefect characteristics.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of this invention, as well as the invention itself,both as to its structure and its operation, will be best understood fromthe accompanying drawings, taken in conjunction with the accompanyingdescription, in which similar reference characters refer to similarparts, and in which:

FIG. 1 is a simplified schematic illustration of one representativeembodiment of a data flow system for a tape drive, the data flow systemincluding a tape layout module that incorporates a tape layoutoptimization system having features of the present invention;

FIG. 2 is a simplified schematic illustration of an embodiment of a dataorganization system that can be utilized within the data flow system,the data organization system illustrating how variable-sized data blocksreceived from a host device can be broken into fixed-sized data sets,and then into smaller fixed-sized subdata sets (SDS));

FIG. 3 is a simplified schematic illustration of an embodiment of a dataprotection system that can be utilized within the data flow system,wherein data of an SDS is organized into a two-dimensional array, withECC parity appended to the SDS array, and with each row of theECC-protected data array being a codeword interleave (CWI);

FIG. 4 is a simplified schematic illustration of a representativeembodiment of a magnetic tape layout of CWIs on the magnetic tape;

FIG. 5 is a simplified schematic illustration of a representativeembodiment of the types of error patterns that may occur within themagnetic tape layout;

FIG. 6A is a representative example of a first tape allocation strategyfor a first SDS;

FIG. 6B is a histogram that illustrates CWI separation distances betweenpairs of CWIs based on the first tape allocation strategy illustrated inFIG. 6A;

FIG. 7A is a representative example of a second tape allocation strategyfor a second SDS;

FIG. 7B is a histogram that illustrates CWI separation distances betweenpairs of CWIs based on the second tape allocation strategy illustratedin FIG. 7A;

FIG. 8 is a flow chart for determining CWI allocation parameters for CWIset swaps and track swaps; and

FIG. 9 is a graphical illustration of CWI separation distance spectrafor a certain tape format applying different numbers of track rotations.

DESCRIPTION

Embodiments of the present invention are described herein in the contextof a tape layout optimization system and method for reliable ErrorCorrection Coding (ECC) decoding that is based on media defectcharacteristics. More particularly, the present invention substantiallyimproves tape layout designs by incorporating side information such asmedia defect/error statistics (i.e. especially media defect/errorstatistics that are repeatable and/or reproducible) into theoptimization problem to achieve the best overall separation betweencodeword interleaves (CWIs) as they are laid out on the tape and bestECC decoding performance. Additionally, the tape layout design isfurther optimized through use of the present invention by creating amore balanced design that takes into consideration separation betweenCWIs for all subdata sets (SDSs).

As described herein, the various steps of the tape layout optimizationsystem and method can be performed in any suitable order to achieve thedesired goal. Additionally, it is appreciated that the system and methoddescribed in detail herein can be implemented through a series ofinstructions to be carried out via one or more computer algorithms.Further, it is also appreciated that the series of instructions may beprovided to a processor of a general-purpose computer, a special-purposecomputer, or another suitable programmable data processing apparatus.The computer algorithms may also be stored in a computer-readablestorage medium or be loaded directly onto a computer or other suitableprogrammable data processing apparatus to cause a series of operationalsteps to be performed by the computer or other programmable apparatus.

Those of ordinary skill in the art will realize that the followingdetailed description of the present invention is illustrative only andis not intended to be in any way limiting. Other embodiments of thepresent invention will readily suggest themselves to such skilledpersons having the benefit of this disclosure. Reference will now bemade in detail to implementations of the present invention asillustrated in the accompanying drawings. The same or similar referenceindicators will be used throughout the drawings and the followingdetailed description to refer to the same or like parts.

In the interest of clarity, not all of the routine features of theimplementations described herein are shown and described. It will, ofcourse, be appreciated that in the development of any such actualimplementations, numerous implementation-specific decisions must be madein order to achieve the developer's specific goals, such as compliancewith application-related and business-related constraints, and thatthese specific goals will vary from one implementation to another andfrom one developer to another. Moreover, it will be appreciated thatsuch a development effort might be complex and time-consuming, but wouldnevertheless be a routine undertaking of engineering for those ofordinary skill in the art having the benefit of this disclosure.

FIG. 1 is a simplified schematic illustration of one representativeexample of a data flow system 100 for a tape drive. The specific dataflow system 100 illustrated in FIG. 1 is presented only as one possiblemethod for data flow to be provided for a tape drive, and is notintended to be limiting in any manner. Moreover, it is appreciated thatother data flows may also benefit from the tape layout optimizationsystem described in detail herein, and such data flow systems andmethods are thus intended to be encompassed within the scope of theinvention.

The design of the data flow system 100 can be varied. In certainembodiments, as shown in FIG. 1, the data flow system 100 can include ahost device 102, a data intake system 104, a data preprocessing system106, a data protection system 108, a tape layout module 110, and alayout processing module 112. Each of the systems and modulesillustrated and described in FIG. 1 can further include one or moresubsystems that work in conjunction with one another to perform theoverall functions of each system and module. Additionally, in some suchembodiments, one or more of the data intake system 104, the datapreprocessing system 106, the data protection system 108, the tapelayout module 110 and the layout processing module 112 can beincorporated within a data processing apparatus 103 (illustrated as adashed box), e.g., a suitable type of computing device. Alternatively,the data flow system 100 can include more systems and modules or fewersystems and modules than those specifically illustrated in FIG. 1. Stillalternatively, it is appreciated that the illustrated flow of datathrough the data flow system 100 shown in FIG. 1 can be performed in adifferent manner, e.g., in a different order, than what is describedherein.

As an overview, the tape layout module 110 is specially configured toenable a substantially improved and/or optimized tape layout forreliable ECC decoding that is based on media defect characteristics.More specifically, in various embodiments, the tape layout module 110includes a tape layout optimization system 111 (illustrated in phantom)having one or more processors 111A (illustrated in phantom) and one ormore circuits 111B (illustrated in phantom) that utilize speciallydesigned computer algorithms for purposes of enabling a substantiallyimproved and/or optimized tape layout for reliable ECC decoding that isbased on media defect characteristics. Additionally, in some suchembodiments, the tape layout optimization system 111 can be configuredto substantially improve and/or optimize the selection and use of atleast one, and possibly a plurality of, layout parameter for purposes oflaying out data, i.e. both logically and physically, on tape. Moreparticularly, as provided herein, the selection and use of the layoutparameter(s) is based at least in part on the identification of mediadefect characteristics that may be present within the tape medium. Thelayout parameter(s) selected by and utilized within the tape layoutoptimization system 111 can include, but are not limited to, trackrotations (TR), CWI set swaps (SS), track swaps (TS), and odd/evenindexed SDS separations (SDSS).

In certain embodiments, the host device 102 can be utilized to provide asequence of bytes contained within variable-length data blocks 214(illustrated in FIG. 2) to the data intake system 104. Thevariable-length data blocks 214 that are provided to the data intakesystem 104 may be any size up to a maximum size supported by a tapedrive. In some embodiments, the data intake system 104 may perform acyclic redundancy check (CRC) on the incoming data blocks 214, and thusmay add any suitable CRC information to these data blocks 214.

The variable-length data blocks 214 are then passed along to the datapreprocessing system 106 where the variable-length data blocks 214 areconverted into a more suitable format for tape layout. For example, incertain embodiments, the variable-length data blocks 214 may becompressed and/or encrypted as desired. Additionally, the datapreprocessing system 106 can also include a data organization system 216(illustrated in FIG. 2).

FIG. 2 is a simplified schematic illustration of an embodiment of thedata organization system 216 that can be utilized within the data flowsystem 100. In particular, within the data organization system 216, thevariable-length data blocks 214, which may or may not have beencompressed and/or encrypted in a suitable manner, are initially brokendown into a plurality of data sets 218 that are of a fixed size. Thenumber of bytes in each data set 218 can be varied depending upon therequirements of the data flow system 100 and/or the tape drive withwhich the data is being used. During this process, the data organizationsystem 216 begins filling a first data set 218 at a first byte of thedata set 218 and continues until a last byte of the data set 218. Thedata organization system 216 continues this process until all of thedata blocks 214 have been filled into the fixed-size data sets 218.Subsequently, the data sets 218 may in turn be broken down into subdatasets 220 (SDS) that are also of a fixed size. The number of bytes ineach subdata set 220 can also be varied depending upon the requirementsof the data flow system 100 and/or the tape drive with which the data isbeing used.

Referring again to FIG. 1, once the variable-length data blocks 214(illustrated in FIG. 2) have been preprocessed within the datapreprocessing system 106 and converted into a plurality of fixed-sizesubdata sets 220, the fixed-size SDS 220 are then passed to the dataprotection system 108.

FIG. 3 is a simplified schematic illustration of an embodiment of thedata protection system 308 that can be utilized within the data flowsystem 100. Initially within the data protection system 308, each SDS220 (illustrated in FIG. 2) may be organized into a two-dimensionalarray of data 322 (illustrated as a block in FIG. 3). The number of rowsand columns, and the size of each row and each column, within thetwo-dimensional array of data 322 can be varied to suit the amount ofdata included within the SDS 220. In particular, in one embodiment, thedata from within the SDS 220 can be used to fill the two-dimensionalarray of data 322 on a row-by-row basis, with each row filling out adesired number of columns. Alternatively, in another embodiment, thedata from within the SDS 220 can be used to fill the two-dimensionalarray of data 322 on a column-by-column basis, with each column fillingout a desired number of rows.

Subsequently, error correction coding (ECC) may be applied to the SDSdata array 322. More particularly, the SDS data array 322 may be passedto a row ECC encoder. The row ECC encoder may generate row ECC paritydata 324 for each row in the SDS data array 322 and append the row ECCparity data 324 to the SDS data array 322. The row ECC parity data 324is illustrated simply as a block positioned adjacent to the SDS dataarray 322. In certain embodiments, headers (not shown) and othermetadata may be appended to each row in the SDS data array 322 prior toutilizing the row ECC encoder to generate the row ECC parity data 324for each row in the SDS data array 322 that is appended to the SDS dataarray 322

Once the row ECC parity data 324 is generated and appended to the SDSdata array 322, the SDS data array 322 may then be passed to a columnECC encoder which generates column ECC parity data 326 for each columnin the SDS data array 322. The column ECC parity data 326 is illustratedsimply as a block positioned below and adjacent to the SDS data array322 and the row ECC parity data 324.

The row ECC parity data 324 protects each row of the SDS data array 322while the column ECC parity data 326 protects each column in the SDSdata array 322. Additionally, in certain embodiments, the row ECC paritydata 324 and/or the column ECC parity data 326 can also protect anyheaders or other metadata that may have been appended to each row in theSDS data array 322. Each row of the ECC-protected data array is nowreferred to as a codeword interleave (CWI).

It is appreciated that in certain applications, due to linearity of theECC, the row ECC parity data 324 and the column ECC parity data 326 canbe appended to the SDS data array 322 in either order. In particular,the row ECC parity data 324 can be appended to the SDS data array 322prior to the column ECC parity data 326, such as is shown in FIG. 3.Alternatively, the column ECC parity data 326 can be appended to the SDSdata array 322 prior to the row ECC parity data 324.

Referring again to FIG. 1, the ECC-protected data array is next passedalong to the tape layout module 110. In particular, the tape layoutmodule 110 is configured to distribute the data array, the ECC parity,and the headers and other metadata, i.e. the CWIs, across differenttracks and in different orders for recording on the magnetic tape. Asprovided in detail herein, the tape layout module 110 can incorporatethe tape layout optimization system 111 that utilizes media defects andcorrelated error statistics to provide the best ECC decoding performancefor the given defect/error model of interest. Additionally, as notedabove, the tape layout optimization system 111 substantially improvesand/or optimizes the selection of type and number of the layoutparameters that may be utilized in the actual layout of the data ontape.

FIG. 4 is a simplified schematic illustration of a representativeembodiment of a tape layout of a plurality of CWIs 428 laid out onmagnetic tape 430. As shown, the magnetic tape 430 can include aplurality of tracks 432 (e.g., 8, 16, or 32 tracks, and illustrated forexample as a dashed box in FIG. 4) that are laid out along the length ofthe magnetic tape 430.

In certain applications, the CWIs 428 are distributed across and alongthe magnetic tape 430 in a number of passes referred to herein as wraps.In each wrap, based on the number of tracks 432, T, on the tape 430, theCWIs 428 can be allocated to each track 432 such that spatiallycorrelated errors or defects on the magnetic tape surface will spreadacross multiple SDSs 220 (illustrated in FIG. 2). In an attempt tominimize the burden on the ECC decoding of each SDS 220, such anallocation will ideally even out the correlated errors that happen onmagnetic tape by distributing CWIs over the distinct SDSs 220. In otherapplications, the tape drive can read and/or write multiple longitudinaltracks 432 on the magnetic tape 430 substantially simultaneously. Forexample, with a magnetic tape 430 including T simultaneously recordedtracks 432, T CWIs 428 are written substantially simultaneously, one CWI428 per track 432. In some such applications, the group ofsimultaneously written CWIs 428 is referred to herein as a CWI set 434(illustrated for example as a dashed box in FIG. 4). Thus, as the tapehead moves along the magnetic tape 430, the CWI sets 434 are read fromor written to the magnetic tape 430. FIG. 4 illustrates a plurality ofCWI sets 434 that have been laid out across the magnetic tape 430.

Also shown in FIG. 4 within the tape layout is an interset distance 436,an intertrack distance 438, and a track width 440. The interset distance436 is the distance from the middle point of one CWI 428 to the middlepoint of the next CWI 428 within a track 432. The intertrack distance438 is the distance from the middle point of one CWI 428 to the middlepoint of the next CWI 428 within a CWI set 434, i.e. from one track 432to the next track 432. The track width 440 is the width of eachindividual track 432. As shown, the interset distance 436 and theintertrack distance 438 are functions of linear density, magnetic tapelength and width. It is appreciated that the specific interset distance436, intertrack distance 438 and track width 440 can vary depending onthe particular tape format being utilized. For example, in certainnon-exclusive alternative embodiments, the interset distance 436 can bebetween approximately 350 μm and 400 μm, the intertrack distance 438 canbe between approximately 70 μm and 90 μm, and the track width can bebetween approximately 1.5 μm and 2.5 μm. Alternatively, the intersetdistance 436, the intertrack distance 438 and the track width 440 canhave values different than those specifically listed herein above.

Additionally, FIG. 4 also shows that a physical CWI separation 442 canbe measured between any pair of CWIs 428 within an SDS 220 as laid outon the magnetic tape 430. For example, if there are N CWIs 428 per SDS220, then there would be N(N−1)/2 different pairs of CWIs 428.Evaluating the CWI separation 442 for the full gamut of pairs of CWIs428 in a given SDS 220 is sometimes referred to as the CWI separationdistance spectra.

In certain applications, the physical CWI separation 442 is defined tobe the physical Euclidian distance between any pair of CWIs 428 within agiven SDS 220 based on their tape allocation, specifically consideringthe midpoint of each CWI 428 as the point of reference. Alternatively,in other applications, the physical CWI separation 442 can be measuredbetween any pairs of CWIs 428 within the SDS 220 by using a differentpoint of reference within the CWI, e.g., a corner-to-corner measurement.

Generally speaking, the greater the physical distance between CWIs 428of the same SDS 220, the less likely it is that a single error eventwill affect more than one CWI 428 in an SDS 220. Thus, as providedherein, one of the main objectives of tape layout designs is to maximizethe minimum separation between CWIs 428 belonging to a particular SDS220. The minimum separation between CWIs 428 can be defined as theminimum CWI separation 442 for all CWI pairs of all SDSs 220 dictated bythe tape layout design format. Unfortunately, considering only theminimum separation may not address the requirements of today's taperecording technology in which the operational performance is exacerbateddue to defects and long correlated error bursts while used with narrowheads. It is appreciated that such media defects and/or dead track orstripe errors can cause different degrees of degradation to the system,especially when the minimum CWI separation 442 is different fordifferent SDSs 220. Various specific embodiments of the tape layoutoptimization system 111 (illustrated in FIG. 1) having features of thepresent invention, which are specially configured to compensate for suchdefects and error types, will be described in greater detail hereinbelow.

Referring again to FIG. 1, once the CWIs 428 (illustrated in FIG. 4)have been laid out on the tape 430 (illustrated in FIG. 4), the datasequences may then be processed in any suitable manner within the layoutprocessing module 112. For example, in some embodiments, the layoutprocessing module 112 may include one or more randomizers which performadditional signal processing on the data, run length limited (RLL)encoders that may then transform the spectra of the information so thatit is better suited for magnetic recording, and multiplexers that maythen multiplex synchronization information, such as variable frequencyoscillators (VFOs), sync characters, or the like, into the informationto enable it to be synchronized when read.

As provided herein, it is appreciated that certain types of errorpatterns may exist as the data is laid out on the magnetic tape 430.FIG. 5 is a simplified schematic illustration of a representativeembodiment of the types of error patterns that may occur within the tapelayout on magnetic tape 530. More particularly, FIG. 5 illustrates threegeneral types of defects/correlated errors that one is likely toencounter within the tape layout, which may be the source of aperformance bottleneck. For example, FIG. 5 illustrates along-trackerrors 550A (illustrated with a series of “x”s) that lie along the tape530, and across-track errors 550B (illustrated with a series of “x”s),or stripe errors, that lie across the magnetic tape 530. The along-trackerrors 550A that occur parallel to the tape 530 may affect multiple CWIs428 (illustrated in FIG. 4) in one or more tracks 432 (illustrated inFIG. 4) along the length of the tape 530. The along-track errors 550Amay be the result of, for example, defective or clogged write or readheads, scratches along the length of the tape 530, manufacturing defectsin the tape 530, debris on the tape 530, changes in environmentalconditions during read/write operations, or the like. The across-trackerrors 550B that occur transverse to the tape 530 may affect multipletracks 432 in a CWI set 434 (illustrated in FIG. 4). The across-trackerrors 550B may be the result of, for example, head tracking problems,scratches across the tape 530, edge damage to the tape 530,manufacturing defects in the tape 530, debris on the tape 530, or thelike.

In addition to the along-track errors 550A and the across-track errors550B, FIG. 5 further illustrates that the tape 530 may include otherrandom errors 550C (illustrated with a series of “x”s) that may occurrandomly transverse to and along the tape 530. These random errors 550Cmay be caused by isolated media defects that arerepeatable/reproducible, and which are typical in magnetic recordingmedia. Examples of such random errors 550C are illustrated in FIG. 5 asbeing captured within generally circular areas on the tape 530. It isappreciated that such circles including the random errors 550C can havea radius r and can happen anywhere on the tape 530. As the radius of thecircle increases, the hazard caused on the ECC decoding becomes elevatedso as to make decoding and retrieving data accurately even moreproblematic.

In one representative example, as noted above, the minimum separation ofCWIs can be defined to be the minimum of all CWI pairs of all SDSsdictated by the tape layout design format. Additionally, assuming that agiven layout design has a minimum separation s_(min), if r<s_(min)/2,then the maximum number of CWIs that belongs to a specific SDS that canbe contained in the circle shown is 1. If all of the defect sizes werelimited to such particular sample defect size, it would be enough toconsider only the minimum CWI separation. However, this may not often bethe case. This argument also demonstrates that the defect size and thedefect appearance frequency (along with its reproducibility) havedifferent effects on the CWIs separated by certain physical distance.The effect on CWIs closely placed on tape is usually larger than theCWIs placed far apart. Thus, such a characterization might be usefulfrom a tape layout design perspective.

Various components, aspects and embodiments of the tape layoutoptimization system 111 (illustrated in FIG. 1) having features of thepresent invention will now be discussed in greater detail. It isunderstood that any of the various components, aspects and embodimentsof the tape layout optimization system 111 as described herein can becombined in any suitable manner to produce even further embodiments.Thus, it is further appreciated that the description of any particularcomponents or aspects of the tape layout optimization system 111 inconjunction with one or more specific embodiments is not intended to belimiting in any manner.

Additionally, knowledge of and assumptions relating to various layoutparameters can be incorporated into the tape layout optimization system111 in order to determine the best tape layout in any given situation.More particularly, it is understood that certain layout parameters arefactored into any embodiment of the tape layout optimization system 111.For example, the layout parameters that can be factored into the tapelayout optimization system 111 include, but are not limited to, thenumber of SDSs in the data to be laid out on the tape, the number oftracks on the tape, the codeword length, the number of track rotations(TR) in terms of CWIs, the number of track swaps (TS), the number of CWIset swaps (SS), and the separation between the CWIs of even/odd indexedSDSs (SDSS).

As part of the tape layout optimization system 111, one of the primaryobjectives of the tape layout design optimization is to make sure thatthe relative CWI separations for each SDS are almost the same. In thismanner, the same ECC decoding performance may be expected for each SDS,and equal protection can be achieved across SDSs for any correlatederror scenarios. Thus, with application of the present invention, it ispossible to provide reliable ECC decoding performance that isapproximately equal across all SDSs within a given data set. Stated inanother manner, use of the present invention takes into considerationCWI separations for each of the SDSs within a given data set foroptimizing the tape layout allocation strategy. By examining the CWIdistance separation for all SDSs within the given data set, the presentinvention is able to generate a tape layout with a more balanced designthat provides better distance properties overall.

In the present invention, since there is no distinguishing between thetype of data in a given data set, there is also no differentiation withthe encoded data when the encoded data is allocated over the physicaltape medium. However, once the desired side information regarding thetype, size and frequency of media defects and statistics (data beingmission critical, vital, sensitive or non-critical) is provided, furtherarrangement can be made and different SDSs can be treated differentlywhile allocating the associated CWIs over the tape surface. This is dueto the understanding that for a particular minimum separation distance,the effect of various defects on different CWIs can be different.

CWI separation distance spectra, as introduced above, is inherited fromcoding theory that considers all pairwise distance between all the CWIsof interest, i.e. all of the CWIs for a given SDS. Additionally, thepresent invention is directed toward a tape layout optimization system111 that evaluates potential tape allocation strategies to determine asubstantially improved and/or optimized tape layout allocation strategyfor a given SDS 220.

As illustrated, for example, in FIGS. 6A and 6B, a histogram showingeach unique CWI separation distance can be made to be able to obtain thedistance spectra of a given tape layout allocation strategy for an SDSof interest. In particular, FIG. 6A is a representative example of afirst tape allocation strategy 652 that could potentially be employedfor a given SDS 220 (illustrated in FIG. 2). Additionally, FIG. 6B is ahistogram that illustrates CWI separation distances between pairs ofCWIs based on the first tape allocation strategy 652 illustrated in FIG.6A. Somewhat similarly, FIG. 7A is a representative example of a secondtape allocation strategy 754 that could potentially be employed for thegiven SDS. Additionally, FIG. 7B is a histogram that illustrates CWIseparation distances between pairs of CWIs based on the second tapeallocation strategy 754 illustrated in FIG. 7A.

In both tape allocation strategies illustrated in FIG. 6A and FIG. 7A,black boxes are utilized to denote all the CWIs that belong to theparticular SDS of interest.

As shown in FIG. 6B and FIG. 7B, for each histogram, the x-axis is usedto show the possible distances between CWIs and the y-axis is used toshow the counts of these distances. For a layout design that has N CWIsper SDS, distance spectra for the individual SDSs is a set representedby

W(S)={w ₁ ,w ₂ , . . . ,w _(N(N-1)/2)}  (Equation 1)

where w_(j) represents the j-th pair of CWIs. Since it is possible tohave two CWI pairs that have the same physical separation, in certainembodiments it is preferred to express the same set with two differentsets B(s)={b₁, b₂, . . . , b_(U)} and C(s)={c₁, c₂, . . . , c_(U)} whereb_(i) represents the i-th unique element of W(s) and c_(i) representsthe count of the unique element b_(i). Hence, the distance spectra canbe plotted by putting B(s) on the x-axis and C(s) on the y-axis.

As provided herein, the CWI distance spectra can be used to evaluate,substantially improve and/or optimize the tape layout allocationstrategy. In other words, the CWI distance spectra can be used as aperformance measure in order to compare different tape layout allocationstrategies. Further, the present invention provides that certain mediadefect statistics are also necessary in addition to the CWI distancespectra before deciding on which design is preferable. For such purpose,a set of coefficients α_(i)(b_(i)) (for i=1, 2, . . . , U) is introducedwhere each coefficient characterizes the effect of distance-i separatedCWIs on the number of CWIs poorly read due to defects and other type ofcorrelated errors. Those coefficients are the result of modeling thedefect characteristics of LTO tapes and media. Such computation is basedon the defect, media type and how often they appear on tape surface.This coefficient can easily be extracted for a given media/drivetechnology combination, e.g., a Media 1/LTO 7 drive combination. Byeliminating the random component of the noise and defects, reproduciblepatterns can determine the core of the coefficient values. It isunderstood that, as shown, the α_(i)'s are functions of the separationdistance b_(i)'s.

Before a final decision is made on a preferred tape layout allocationstrategy, distance spectra information is combined with thesedata-driven coefficients, and a weighted separation coefficient (WSC) iscomputed for the given SDS (indexed by “s”) as follows:

WSC(s)=α₁(b ₁)c ₁+α₂(b ₂)c ₂+ . . . α_(U)(b _(U))c _(U)  (Equation 2)

For this particular example, i.e. comparing the tape layout allocationstrategies illustrated in FIGS. 6A and 7A, it is assumed that the numberof SDSs, S, the number of tracks, T, and the codeword length, N, arefixed and cannot be changed. Accordingly, the final choice for optimaltape layout would be based on the particular choice of layout parameterselections, e.g., track rotations, CWI set swaps, track swaps and SDSseparations, such that WSC(0), WSC(1), . . . WSC(S−1) are jointlyminimized. It is appreciated that for some designs these weightedseparation coefficients for different SDSs might be different i.e., thatparticular design allocates the burden due to defects unequally amongdifferent SDSs. Thus, different ECC decodings will end up with differentdecoding performances in such cases.

In alternative designs, the tape layout can include a balanced design,i.e. where the WSC values for each SDS are weighted substantiallyequally to one another, or an unbalanced design, i.e. where the WSCvalues for each SDS are not weighted equally to one another.

In a first example, the tape layout is assumed to include a balanceddesign. Additionally, for illustration purposes, the following sample(made-up) statistics can be used for U=5,

α₁ = 0.83 α₂ = 0.79 α₃ = 0.71 α₄ = 0.22 α₅ = 0.02with the example distance spectra is as shown in FIGS. 6A and 7A. Sinceit is a balanced design, it is assumed that both designs satisfyWSC(0)=WSC(1)= . . . =WSC(S−1). Thus, the cost function could be the sumof WSCs i.e., Σ_(i)WSC(i) with this constraint. Standard linearprogramming tools can be applied to solve for the solution (maximizationin this case) for the required spectra. However, mapping this solutionto required parameters of the layout design is an integer programmingproblem and cannot be solved in polynomial time.

Since the distance spectra are both given for two designs shown in thisexample (and they are not necessarily optimal) and it is assumed toinclude balanced designs, it is possible to only focus on WSC(0). Incomputing WSC(0)s for both designs using Equation (2) above, it isdetermined that:

Design 1: WSC(0)=17.15

Design 2: WSC(0)=17.54

As a conclusion, it can be seen that Design 1 is preferable given thedistance spectrum and defect characteristics of the tape (i.e. WSC(0) islower for Design 1), although Design 1 has a minimum separation distanceof 1 whereas Design 2 has a minimum separation distance of 2. Thisexample shows in particular, an optimal design should take care of thestatistics of defects and media/correlated errors as well.

Note that this approach with α₁=1, and α_(i)=0 for all other i, reducesthe problem down to looking at minimum-separation-only approach, whendeciding on a good tape layout. Thus, it is apparent that here a moregeneralized version of the previous design approaches is being proposed.

In a second example, the tape layout is assumed to include an unbalanceddesign. Stated in another manner, in some designs, WSC(0)≠WSC(1)≠ . . .≠WSC(S−1) or maybe WSCs may be an ordered sequence depending on therequirements of the system. In this case, the cost function is stillgiven by Σ_(i)WSC(i) and yet the constraint(s) can be imposed by therequirements of the application. For instance, different data typesmight be stored and sensitivity profiles of these data might not match.In that case, SDSs that bear mission critical information are allocatedto the safe partitions/location of the tape for better reliability oraccessibility.

Assuming S=4, and utilizing the same proposed tape layout allocationstrategies shown in FIGS. 6A and 7A, we calculate WSC values as shown inthe following table:

WSC(0) WSC(1) WSC(2) WSC(3) WSC(4) Design 1 17.15 17.15 18.05 18.0517.55 Design 2 17.54 17.54 18.05 18.05 18.23

As can be seen in this table, Design 1 always has smaller or equal WSCfor all the SDSs. Therefore, Design 1 can be said to be a better designthan Design 2. However, it might have been the case that some of theWSCs of SDSs of Design 1 are larger than that of the Design 2. In thatcase, it is more challenging to determine which design is preferablefrom a collective (considering all the SDSs) ECC decoding perspective.In that particular case, the relationship between sensitivity profile ofthe data, WSC and ECC decoding should also be analyzed.

If SDSs bear equally important information from a user perspective, itis advisable to consider WSC(0), WSC(1), . . . WSC(S−1) all together andgenerate one separation distance spectrum for WSC computation.

Based on the example layouts and associated distance spectra and mediadefects illustrated in FIGS. 6A-6B and FIGS. 7A-7B above, asubstantially improved and/or optimized tape layout allocation strategywas chosen. However, as provided herein, it is desired to create andutilize a tape layout optimization system that can provide a moregeneralized method for CWI allocation. For such a tape layoutoptimization system, it is typically necessary to explicitly define thelayout parameters of the layout design that can be substantiallyimproved and/or optimized based on the optimal spectra to be found usingthe ideas/techniques provided above. Again, it is assumed that thenumber of SDS: S, number of tracks: T and codeword length N are thegiven parameters, set by different parties and cannot be changed. Thus,the following layout parameters are subject to optimization:

-   -   1) TR: Track rotation in terms of CWIs    -   2) TS: Number of Track swaps    -   3) SS: Number of CWI set swaps    -   4) SDSS: The separation between the CWIs of even/odd indexed        SDSs

It is understood that track swaps and set swaps may or may not beapplied in any given situation. Here is provided a generic procedure todetermine whether or not to employ swaps. At the beginning of thealgorithm, the possible swaps are initially set to CWI set swap=0 andTrack swap=0. Subsequently, the following procedure is utilized formaking a decision on enabling the swaps. If swaps are allowed, then itis understood that TS and SS parameters also need to be determined.These parameters are usually determined by reasonable choices so as tominimize the number of parameters subject to optimization. For instance,the following procedure can be used to determine TS and SS and hence TRand SDSS will have to be substantially improved and/or optimized asdescribed further below. More specifically, FIG. 8 is a flow chart fordetermining CWI allocation parameters for CWI set swaps and track swaps.

-   -   If Track swap=1 after the procedure, we have TS=M/T/2−1 unless        otherwise stated.    -   If CWI set swap=1 after the procedure, SS=M/T−1 unless otherwise        stated. For example for better CWI separation SS can be set to 1        without looking at the CWI set swap.    -   If CWI set swap=0 after the procedure, SS=1. Usually the half        point in data set is chosen to do the single set swap.

After deciding on the swaps, TR and SDSS can be substantially improvedand/or optimized to meet some optimization criterion using the defectstatistics as explained in detail above. In fact, these layoutparameters are integers and the optimization problem may require realnumbers. In certain embodiments, the tape layout optimization system caneither use relaxation methods for integer programming to generateeffective solutions or use an exhaustive search on the good set ofparameters to substantially improve and/or optimized the layout throughrunning simulations.

Here another representative example is pursued, which generatesnumerical results using LTO tape layouts. For example, the distancespectra for LTO 6 Tape Layout with different track rotations can beutilized (Note that TR=6 is what the LTO 6 format adapted). It isappreciated that CWI allocation tables are not specifically providedherein as they may occupy a lot of space, and may otherwise obscure whatis intended as the present invention. For this particular example,certain parameters are set at T=16, S=32, and N=96, and the generalmethodology set out in detail above is utilized. It is further assumedthat there is an inter-track distance of 166u and an inter-set distanceof 360u, which are based on LTO 6 density operating points. It isappreciated that these specific numbers are being utilized simply forpurposes of demonstration, and the numbers can be varied based on thespecific tape format being utilized. Since each SDS is equally importantfrom a storage point of view, WSC(0), WSC(1), . . . , WSC(31) areconsidered all together, with one CWI separation distance spectrum beingcreated as shown in FIG. 9 for TR=5 and TR=6 with SDSS 2. Moreparticularly, FIG. 9 is a graphical illustration of CWI separationdistance spectra for a certain tape format applying different numbers oftrack rotations. As illustrated, the CWI separation distance spectra forLTO 6 tape format using TR set at 5 is shown in a dashed line, and theCWI separation distance spectra for LTO 6 tape format using TR set at 6is shown in a solid line.

Since each separation point has different vulnerability to defects andcorrelated errors, it is understood that the α_(i) values are different.In this example, it is assumed that:

α₁=0.83, α₂=0.79, α₃=0.71, α₄=0.22, α₅=0.02 and α_(i>5)=0

In computing the WSC for TR=5 and TR=6, it is shown that the design withTR=5 has a WSC of ˜1610 whereas the design with TR=6 has a WSC of ˜150.As can be seen, the design with TR=5 gives better separation distanceproperties given the defect statistics. If the coefficients had insteadbeen set at α₁=1.00, α_(i>1)=0, in other words, if only minimumseparation distance had been considered, the conclusion would notchange. However, in that case, WSCs will be 55 and 25, respectively.Note that the difference is not significant anymore.

As provided herein, using the tape layout optimization system havingfeatures of the present invention, certain advantages can be realized.In particular, based on the apparatus and stated claims in thisdisclosure, a more robust and adaptive tape layout design shall beobtained. The present disclosure has also introduced performancemeasures to compare different layouts. Based on the proposal andperformance metrics provided herein, it can be demonstrated that adesign that takes into account the actual error statistics whileoptimizing the parameters of the design layout will not only benefitcurrent LTO tape formats, but also LTO tapes down the road. Morespecifically, the tape layout optimization system as disclosed herein isbetter able to provide a more balanced design with better overalldistance properties than competing layout systems. The present tapelayout optimization system and method can also potentially increase datareliability or enable increased operating linear densities or smallerhead widths/characteristics for a given reliability level.

Additionally, it is understood that although a number of differentembodiments of the tape layout optimization system 111 have beenillustrated and described herein, one or more features of any oneembodiment can be combined with one or more features of one or more ofthe other embodiments, provided that such combination satisfies theintent of the present invention.

While a number of exemplary aspects and embodiments of the tape layoutoptimization system 111 have been discussed above, those of skill in theart will recognize certain modifications, permutations, additions andsub-combinations thereof. It is therefore intended that the followingappended claims and claims hereafter introduced are interpreted toinclude all such modifications, permutations, additions andsub-combinations as are within their true spirit and scope.

1-19. (canceled)
 20. A magnetic tape for use in a tape drive, themagnetic tape comprising: a plurality of tracks that are laid out alonga length of the magnetic tape, each of the plurality of tracks beingconfigured to receive data, the data being organized into a plurality offixed-size subdata sets with each of the plurality of subdata setsincluding a plurality of codeword interleaves; and a plurality of mediadefect characteristics; wherein the data is laid out on the plurality oftracks in accordance with a tape layout allocation strategy asdetermined by a tape layout module, the tape layout module including: atape layout optimization system including a processor that receivesinformation on the plurality of media defect characteristics, the tapelayout optimization system determining the tape layout allocationstrategy based at least in part on at least one of the plurality ofmedia defect characteristics, and the tape layout optimization systemdetermining the tape layout allocation strategy further based ondistance spectra between pairs of the plurality of codeword interleaves.21. The magnetic tape of claim 20 wherein the tape layout optimizationsystem determines the tape layout allocation strategy based at least inpart on each of the plurality of media defect characteristics.
 22. Themagnetic tape of claim 20 wherein the plurality of media defectcharacteristics are reproducible.
 23. The magnetic tape of claim 20wherein the tape layout optimization system generates a plurality ofcoefficients, α_(i)(b_(i)), that are the result of a modeling of theplurality of media defect characteristics.
 24. The magnetic tape ofclaim 23 wherein the tape layout optimization system determines the tapelayout allocation strategy by computing a weighted separationcoefficient (WSC), WSC(s)=α₁(b₁) c₁+α₂(b₂) c₂+ . . . α_(U)(b_(U)) c_(U),where b_(i) represents the i-th unique element of a distance spectrabetween pairs of the plurality of codeword interleaves, a represents thecount of the unique element b_(i), and U represents the set of allpossible distances for a given layout.
 25. The magnetic tape of claim 20wherein the tape layout optimization system determines the tape layoutallocation strategy by selectively utilizing at least one tape layoutparameter.
 26. The magnetic tape of claim 25 wherein the tape layoutoptimization system determines the tape layout allocation strategy byselectively utilizing a plurality of tape layout parameters.
 27. Themagnetic tape of claim 26 wherein the plurality of tape layoutparameters are selected from a group consisting of track swaps, codewordinterleave set swaps, track rotations, and odd/even indexed subdata setseparations.
 28. A magnetic tape for use in a tape drive, the magnetictape comprising: a plurality of tracks that are laid out along a lengthof the magnetic tape, each of the plurality of tracks being configuredto receive data, the data being organized into a plurality of fixed-sizesubdata sets with each of the plurality of subdata sets including aplurality of codeword interleaves; and a plurality of media defectcharacteristics; wherein the data is laid out on the plurality of tracksin accordance with a tape layout allocation strategy as determined by atape layout module, the tape layout module including: a tape layoutoptimization system including a processor that receives information onthe plurality of media defect characteristics, the tape layoutoptimization system determining the tape layout allocation strategybased at least in part on at least one of the plurality of media defectcharacteristics; and the tape layout optimization system generating aplurality of coefficients, α_(i)(b_(i)), that are the result of amodeling of the plurality of media defect characteristics.
 29. Themagnetic tape of claim 28 wherein the tape layout optimization systemdetermines the tape layout allocation strategy by computing a weightedseparation coefficient (WSC), WSC(s)=α₁(b₁) c₁+α₂(b₂) c₂+ . . .+a_(U)(b_(U)) c_(U), where b_(i) represents the i-th unique element of adistance spectra between pairs of the plurality of codeword interleaves,a represents the count of the unique element b_(i), and U represents theset of all possible distances for a given layout.
 30. The magnetic tapeof claim 28 wherein the tape layout optimization system determines thetape layout allocation strategy based at least in part on each of theplurality of media defect characteristics.
 31. The magnetic tape ofclaim 28 wherein the plurality of media defect characteristics arereproducible.
 32. The magnetic tape of claim 28 wherein the tape layoutoptimization system determines the tape layout allocation strategy byselectively utilizing at least one tape layout parameter.
 33. Themagnetic tape of claim 32 wherein the tape layout optimization systemdetermines the tape layout allocation strategy by selectively utilizinga plurality of tape layout parameters.
 34. The magnetic tape of claim 33wherein the plurality of tape layout parameters are selected from agroup consisting of track swaps, codeword interleave set swaps, trackrotations, and odd/even indexed subdata set separations.
 35. A methodfor manufacturing a magnetic tape usable in a tape drive, the magnetictape including a plurality of media defect characteristics, the methodcomprising: laying out a plurality of tracks along a length of themagnetic tape, each of the plurality of tracks being configured toreceive data, the data being organized into a plurality of fixed-sizesubdata sets with each of the plurality of subdata sets including aplurality of codeword interleaves; and laying out the data on theplurality of tracks in accordance with a tape layout allocation strategyas determined by a tape layout module; wherein the tape layout moduleincludes a tape layout optimization system including a processor thatreceives information on the plurality of media defect characteristics,the tape layout optimization system determining the tape layoutallocation strategy based at least in part on at least one of theplurality of media defect characteristics; and wherein the tape layoutoptimization system determines the tape layout allocation strategyfurther based on distance spectra between pairs of the plurality ofcodeword interleaves.
 36. The method of claim 35 wherein the pluralityof media defect characteristics are reproducible.
 37. The method ofclaim 35 wherein laying out the data includes the tape layoutoptimization system generating a plurality of coefficients,α_(i)(b_(i)), that are the result of a modeling of the plurality ofmedia defect characteristics.
 38. The method of claim 37 wherein layingout the data includes the tape layout optimization system determiningthe tape layout allocation strategy by computing a weighted separationcoefficient (WSC), WSC(s)=α₁(b₁) c₁+α₂(b₂) c₂+ . . . +α_(U)(b_(U))c_(U), where b_(i) represents the i-th unique element of a distancespectra between pairs of the plurality of codeword interleaves, c_(i)represents the count of the unique element b_(i), and U represents theset of all possible distances for a given layout.
 39. The method ofclaim 35 wherein laying out the data includes the tape layoutoptimization system determining the tape layout allocation strategy byselectively utilizing a plurality of tape layout parameters that areselected from a group consisting of track swaps, codeword interleave setswaps, track rotations, and odd/even indexed subdata set separations.